Efficient solution of Poisson's equation using discrete variable representation basis sets for Car-Parrinello ab initio molecular dynamics simulations with cluster boundary conditions

An efficient computational approach to perform Car-Parrinello ab initio molecular dynamics (CPAIMD) simulations under cluster (free) boundary conditions is presented. The general approach builds upon a recent real-space CPAIMD formalism using discrete variable representation (DVR) basis sets [Y. Liu, Phys. Rev. B 12, 125110 (2003); H.-S. Lee and M. E. Tuckerman, J. Phys. Chem. A 110, 5549 (2006)]. In order to satisfy cluster boundary conditions, a DVR based on sinc functions is utilized to expand the Kohn-Sham orbitals and electron density. Poisson's equation is solved in order to calculate the Hartree potential via an integral representation of the 1r singularity. Excellent convergence properties are achieved with respect to the number of grid points (or DVR functions) and the size of the simulation cell. A straightforward implementation of the present approach leads to near linear scaling [O (N ⁴³)] of the computational cost with respect to the system size (N) for the solution of Poisson's equation. The accuracy and stability of CPAIMD simulations based on sinc DVR are tested for a model problem as well as for N₂ and a water dimer.